For questions on dice, a small throwable object with multiple resting positions, used for generating random numbers. This makes dice suitable as gambling devices for games like craps, or for use in non-gambling tabletop games.
13
votes
1answer
119 views
Generalized nontransitive dice
Let $X_1, \ldots, X_n$ be a collection of random variables. Consider the directed graph with vertex set $\{ 1, 2, \ldots, n \}$ where there is a directed edge $i \to j$ if $\mathbb{P}(X_i > X_j) ...
1
vote
1answer
29 views
Dice probability when a number is disallowed in the first round
In the game Settlers of Catan a player starts each turn rolling 2 six sided dice. There's a variation of the game where if a 7 is rolled in the first round of a game (a 'round' is when each player has ...
1
vote
1answer
22 views
Dice tracker and roll probability percentage
I have a dice tracker that graphs the combined roll of 2 fair six sided dice (numbers 2 through 12). I want to display the variance percentage that the current number is over/under as a ...
4
votes
1answer
37 views
Deduce dice configuration knowing 2 adjacent faces
Let's say I have a die. I know it's up face and right face. I'd like to know what's on other faces, in this configuration.
I know the dice configuration:
...
2
votes
1answer
46 views
Probability of rolling $n$ successes on an open-ended/exploding dice roll
I'm trying to compute the probability of achieving a certain number of successes when rolling a die pool for both open-ended/exploding and closed tests. Success is defined as a roll above a certain ...
1
vote
2answers
35 views
Coinflip statistics
There is a betting strategy for coinflips, called Martingale, in which the player should pick heads or tails and keep betting on it (doubling their bet on every loss) to eventually make a win when it ...
0
votes
4answers
47 views
Probability of $X$ out of $N$ dice landing on $M$
The problem is as follows:
We have $N$ dice and we throw them on a table. What is the probability that $M$ will fall $X$ times?
Specific example:
We have $10$ dice and we throw them on a table. What ...
0
votes
2answers
136 views
Probability of gaining more than $\$20$ in a two person die game
Jack and Jill gamble on a roll of a die, as follows. If the die shows $1$ or $2$ spots, Jack gives Jill $\$1$. If the die shows $5$ or $6$ spots, Jill gives Jack $\$1$. If the die shows $3$ or $4$ ...
1
vote
1answer
21 views
Determining the probability of throwing $8$ with two dice
Suppose we have two dice. Now we are imposing a condition that the two dice are independent of each other and when we throw, we must have $8$ (that means $6+2 , 5+3$ or $4+4$ etc). Therefore we are ...
1
vote
0answers
35 views
How do you calculate the probability of army loss in Risk, but with modifiers to dice?
I was wondering how you can calculate the outcome of dice rolls in the board game Risk, but with modifiers, assuming 3 attackers and 2 defenders.
In Risk the attacker rolls 3 dice, and the defender ...
-12
votes
0answers
158 views
Help me solve this problem (Die related) [closed]
A die is rolled 60 times.
A)Find the expected number of times the face with 6 spots appears.
B)Find the SE of the number of times the face with 6 spots appears.
C)Find the normal approximation to the ...
3
votes
1answer
71 views
30-sided die, 2-player game
Two players play a game. Player 1 goes first, and chooses a number between 1 and 30 (inclusive). Player 2 chooses second; he can't choose Player 1's number. A fair 30-sided die is rolled. The player ...
5
votes
2answers
68 views
100-sided die probability
The question is as follows: You are given a 100-sided die. After you roll once, you can choose to either get paid the dollar amount of that roll OR pay one dollar for one more roll. What is the ...
4
votes
2answers
109 views
3 Die Probability
The number of times you have to roll a set of 3 die to see a 6 on each die appears to be around ~10.555 according to a implementation of this in c++ and c#. How would this be statistically proven as ...
2
votes
2answers
81 views
The Carnival Dice game
I was reading through an elementary mathematics book lately. The author claims that every probability question, no matter how intimidating it may look, can be solved using a four-step method:
...
4
votes
2answers
82 views
Rolling a fair die 4 times, what is the probability of getting an increasing sequence of numbers?
Game: I roll a die 4 times. What is the probability that I get a strictly increasing sequence of numbers.
My initial thought is as follows: we condition on R1 (the first roll) being a 1, 2, or 3 ...
3
votes
1answer
41 views
Player 1 and Player 2 toss n and m fair dice respectively. What is the probability that there's no single coincidence between their results.
Coincidences within results of each player are possible.
Example of "successful" event (n=m=3): {1,1,6} and {3,4,5} (no coincidences)
Example of "unsuccessful" event (n=m=3): {1,2,6} and {2,4,5} (1 ...
0
votes
1answer
32 views
Expected number of different faces in multiple die roles
I roll 6 6-sided regular dice. What is the expected number of unique up-facing sides I will find among those dice?
1
vote
2answers
45 views
Rolling dice Probability that Sum
If 10 pairs of fair dice are rolled, approximate the probability that the sum of the
values obtained (which ranges from 20 to 120) is between 30 and 40 inclusive.
I dont know where to start with this ...
5
votes
1answer
104 views
What are fair point values for Zombie dice?
Described below is a modified version of Zombie dice ( http://www.sjgames.com/dice/zombiedice/ ) which the kids and I play.
As in the original game, the idea is to sequentially roll sets of 3 ...
0
votes
1answer
65 views
Statistics question on probability
Suppose that one hundred fair dice are tossed. Estimate the probability that the sum of the faces showing exceeds 370. Include a continuity correction in your analysis.
1
vote
3answers
65 views
Probability of a dice game
Here is my question... n players playing a dice game which any of them who trows a 6 the game is over and he wins. They do it 1 by 1 .So what is the probabilty of winning for any 1 of them ?
My ...
7
votes
2answers
59 views
Three equal die rolls in a row in a $3\times 3$ array
If 9 six-sided dice were rolled consecutively and displayed in a $3\times3$ format, what is the probability of a line of 3 of the same number occurring? Considering the 8 ways that are possible; 3 ...
2
votes
2answers
61 views
Probability of winning blackjack dice game?
I know a little bit about probability but I am not sure how to calculate this:
In a dice game of blackjack, there are two parties. The player and the dealer. The aim of this game is to get as ...
2
votes
2answers
102 views
Solve for numbers to appear on two six-sided dice
I have a small wooden calendar that uses two six-sided dice to display day of month. One die carries numbers 0, 1, 2, 6, 7, 8 and the other carries 0, 1, 2, 3, 4, 5. The six of course doubles as the ...
0
votes
1answer
117 views
Dice question: Probability of rolling at least 2 of 3 dice with score 3 or less
my first post here.
I've recently gotten back to boardgaming (Labyrinth: The War on Terror in this case) and would like to get clear on the probability of various actions. I've learnt about 'basic' ...
4
votes
1answer
66 views
Dice game modelling: Lose everything on “3”, double everything on “1” or “6”
I was recently playing a quite easy dice game:
You trow a fair dice: if you get a "3" the next player continues, if you get something else it is up to you to continue. If you continue and you throw ...
0
votes
1answer
46 views
Finding range, partiton and finding the dependency of a random variable
How to do this question
part (a)
range(X) =(2,3,4,5,....12) right the range is usually from 2 to 12
range(y) =(2,3,4,5,6) the range is usually from two to 6 right?
range(z) = (0,1,2,3,4,5)
...
2
votes
4answers
283 views
Probability of rolling three dice without getting a 6
I am having trouble understanding how you get $91/216$ as the answer to this question.
say a die is rolled three times
what is the probability that at least one roll is 6?
2
votes
1answer
73 views
Two dice roll questions related to rolling a Yahtzee
I watched a video on youtube which stated the probability of rolling a yahtzee in a single roll (same value on 5 six sided dice) before 1296 rolls is 63%. The probability of rolling a yahtzee on any ...
2
votes
2answers
57 views
Yahtzee large straight strategy.
I've recently got into playing Yahtzee with my brother. During a game we had on my first roll for my last round I got (5 4 4 2 1). I only had my large straight left, so naturally I was hopeful with ...
0
votes
3answers
29 views
probability proof requiring conditional probability
Consider the experiment where two dice are thrown. Let $A$ be the event that the sum of the two dice is 7. For each $i\in\{1,2,3,4,5,6\}$, let $B_i$ be the event that at least one $i$ is thrown.
...
1
vote
1answer
666 views
Rolling 2 fair, 6 sided dice find P(sum=12, 2times in 36 rolls)
I have a dice problem.
If we roll 2 fair dice, and the sum is 12 then our test is a pass, otherwise its a fail.
What is the probability that the number of passes in 36 tests is greater then 1.
...
0
votes
1answer
45 views
Probability of a unplayable layout in a boardgame
I was at the store the other day and saw a game called Rubik's Race. The game consist of: two 5x5 sliding puzzle boards each populated with 4 tiles of each of the 6 colors of a Rubik's cube, 9 six ...
0
votes
1answer
53 views
Rolling 5, 6 sided dice where top 3 equal 15. How many rolls? How in Recursion?
Let's say that I have 5 (n), 6-sided (d) normal dice. How would I figure out how many possible rolls there are, where the top 3 (k) numbers rolled, equal 15 (t)? How would I do this using recursion ...
5
votes
2answers
105 views
Choosing between $n$ things using dice?
For which $n$ is there a finite algorithm to choose between $n$ things with the same probability using a die?
For example, we can choose between 2 things, 3 things, 4 things, 6 things, and 8 things, ...
1
vote
1answer
109 views
What's the optimal strategy of this dice game?
I'm working on dynamic programming problems this week. The following is a dice game. I'm trying to find the optimal strategy using dynamic programming.
The game's description :
The player rolls ...
3
votes
2answers
129 views
What's the optimal strategy of this dice game?
I'm working on a dynamic programming problem. I want to find the optimal strategy and simulate it.
The game's description:
The player rolls two dice.
If the numbers shown by the two dice are ...
1
vote
1answer
87 views
Probability of A given B & C?
I would like to sum the probability that given 3 (potentially biased) die rolls, all 3 rolls will be different-- what is the correct way to do this?
So far, I have:
$$
1 - ...
0
votes
2answers
66 views
Probability of dice double - why not count duplicates?
What is the probability of getting double dice? (one throw)
All possible dice rolls are 36 (counting even rolls like 1-4 and 4-1).
But when counting the doubles, why not count 1-1 twice, for ...
1
vote
2answers
224 views
Probability, Expected Value and Variance of a Dice Roll
Roll 5 fair six sided dice. Let X be the number of sixes.
1) Find $\ P(X=2)$
2) Find $\ P(X <= 1)$
3) Find $\ E[X]$
4) Find $\ Var(X)$
I've been able to find the first two answers on ...
1
vote
1answer
95 views
Find E[N]. (Absorbing States MC)
Assume we toss a dice until odd number appears four consecutive times, and in such a case we stop the game. Let $N$ be the total number of times we will toss the dice. Find $E[N]$.
Lets say for ...
0
votes
0answers
22 views
Expected value of throws for N-sided dice [duplicate]
Possible Duplicate:
Expected time to roll all 1 through 6 on a die
"In a game of fair N sided dice throw what is the expected number of throws to make sure that all N outcomes appear at ...
1
vote
1answer
183 views
Probability problem of dice game
I heard a problem from a riddle book:
$A$ and $B$ roll two standard dice and record the sum of two numbers. $A$ wins when two consecutive outcomes are $7$ and $B$ wins when three consecutive outcomes ...
2
votes
0answers
86 views
probability of rolling at least $n$ on $k$ 6-sided dice
Is there a simple form for the probability of rolling at least $n$ on $k$ 6-sided dice? Of course you can do it by recursion (see here). But is there a way to do it with just a few binomial ...
5
votes
2answers
166 views
Multiple dice rolls (D&D Skill challenge)
In Dungeons and Dragons there is something called a skill challenge, which involves rolling some dice (no surprise there).
An example of a skill challenge:
Skill challenge DC 25 thievery. Roll a d20* ...
3
votes
2answers
60 views
What are the probabilities in this particular spin-off of BlackJack
A few of my friends are playing on a gaming server where this game exists. I was curious about the probabilities in it but i was unable to derive them.
Any help would be MUCH appreciated.
Note: For ...
2
votes
1answer
553 views
Probability of rolling the same number twice
Math novice here. With a 10-sided die, the probably of rolling '1' is 10%. I'm tempted to think the probability of rolling '1' with two consecutive rolls is 20%. Would I be correct?
Not sure if I ...
5
votes
1answer
137 views
What are the probabilities of a tie when rolling to see who goes first in a board games for various numbers of dice and various numbers of players?
When playing many board games, the first step is to have everyone roll a die to see who goes first, with a roll off in the case of a tie. While doing that over the Christmas break, my husband ...
4
votes
1answer
124 views
Probability of a certain dice roll sum disregarding lowest rolls
The number of ways to obtain a total of $p$ in $n$ rolls of $s$-sided dice is:
$$c=\sum_{k=0}^{\lfloor(p-n)/s\rfloor}(-1)^k\binom{n}k\binom{p-sk-1}{n-1}\;.$$
What I'm interested in is making the $n$ ...
